- PhD, Dartmouth College, 2012
- MA, Dartmouth College, 2009
- MA, University of Pennsylvania, 2006
- BA, University of Pennsylvania, 2006
My research is concerned primarily with the theory of arithmetic groups, a fascinating area lying at the intersection of algebraic number theory and differential geometry. Much of my work involves the application of ideas from algebraic or analytic number theory in order to prove results of a geometric or topological nature.
More explicitly, I am interested in the geometry and topology of arithmetic hyperbolic manifolds and more generally, arithmetic locally symmetric spaces. In particular, I like to consider questions which arise in spectral geometry; that is, the extent to which one can ‘‘hear’’ the geometry of a manifold given knowledge of its Laplace eigenvalue spectrum or geodesic length spectrum.
Perhaps surprisingly, these questions can often be reduced to problems in algebraic and analytic number theory relating to things like orders in central simple algebras, the structure of affine buildings and Mahler measures of algebraic integers.
- MATH 231-01. Multivariable Calculus
- MATH 231-02. Multivariable Calculus
- MATH 350-01. Geometry